10 Axiomas de Algebra Lineal

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Questions and Answers

Qual é la definizione de Closure Under Addition?

  • U+V = V+U
  • U+(-U) = (0 vector)
  • U+V = U
  • U+V = in le spatio vectorial (correct)

Qual es la definizione de Communitive Property?

U+V = V+U

Qual es la definizione de Associative Property?

U+(V+W) = (U+V)+W

Qual es la definizione de Additive Identity?

<p>U+(0 vector) = U</p> Signup and view all the answers

Qual es la definizione de Additive Inverse?

<p>U+(-U) = (0 vector)</p> Signup and view all the answers

Qual é la definizione de Closure under multiplication?

<p>C*U = in le spatio vectorial (D)</p> Signup and view all the answers

Qual es la definizione de Distributive Property (C(U+V))?

<p>C(U+V) = CU+CV</p> Signup and view all the answers

Qual es la definizione de Distributive Property (U(C+D))?

<p>U(C+D) = UC+UD</p> Signup and view all the answers

Qual es la definizione de Associative Property (C(D*U))?

<p>C(D<em>U) = C</em>D(U)</p> Signup and view all the answers

Qual es la definizione de Multiplication Identity?

<p>(1)*U = U</p> Signup and view all the answers

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Study Notes

Proprietates de Espacios Vectorial

  • Closure Under Addition: Si U e V es vectores, alors U+V pertene al espacio vectorial.

  • Proprietate Commutativ: La addition de vectores es commutativ, implicante que U+V es equal a V+U.

  • Proprietate Associativ: La addition es associativ, significa que U+(V+W) es equal a (U+V)+W.

  • Identitate Additiv: Exista un vetor null, 0, tal que U+(0 vector) resulta in U, mantenente U invariabil.

  • Inverse Additiv: Per cada vetor U, existe un vetor -U tal que U+(-U) resulta in (0 vector).

  • Closure Under Multiplication: Multiplicando un escalar C con un vetor U resulta in un prodotto que pertenece al espacio vectorial.

  • Proprietate Distributiv (Addition): Multiplicando un escalar C con la suma de dos vectores U e V resulta in C(U+V) = CU + CV.

  • Proprietate Distributiv (Escalar): Multiplicando un vetor U con la somma de dos scalares C e D resulta in U(C+D) = UC + UD.

  • Proprietate Associativ (Multiplicacion): Multiplicando un escalar C con un producto DU resulta in C(DU) = C*D(U).

  • Identitate Multiplicativ: Multiplicando un vetor U per l'escalaire 1 produz U invariabil, (1)*U = U.

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